CAREER: Dynamics by Design: Bifurcation Engineering for Sensors and Structures

About This Grant

Sensors with high resolution and detection capabilities have the potential to transform applications in many facets of Americans' lives, including enabling new cancer screenings, earthquake early warnings, and expanding the lifetime of next-generation aircraft. Advances in these areas can be enabled by nonlinear dynamic behavior—sharp state transitions, threshold sensitivity, and multi-stable response that exceed what linear designs can achieve. While decades of research have produced deep understanding of these phenomena, the corresponding design question remains open: given a desired nonlinear response, how should a system be configured to produce it? This Faculty Early Career Development Program (CAREER) grant supports research answering this question by establishing mathematical and computational foundations for bifurcation engineering—the systematic design of the qualitative transitions governing when systems switch equilibrium states, lose stability, or exhibit the sharp responses central to precision measurement and control. By converting nonlinear device development from a specialist craft into a transferable methodology and providing open-source tools, this research advances the national health, prosperity, and welfare by accelerating innovations in environmental monitoring, medical diagnostics, and infrastructure resilience. Integrated with these research activities, this grant supports educational initiatives engaging K-12 students and the general public through science center and library exhibits, enriching undergraduate and graduate curricula with nonlinear design methods, and broadening participation in STEM through layered mentorship spanning multiple educational levels. Although powerful tools exist for characterizing nonlinear dynamical systems, they have not yet been extended to the inverse problem of designing systems that achieve specified response characteristics. Doing so requires overcoming interrelated challenges: responses depend sensitively on parameters, undergo qualitative changes at critical parameter values, and involve multiple coexisting solutions whose selection depends on history. This research develops a unified framework for inverse design via bifurcation engineering, organized around three thrusts. The first formulates mathematical representations treating bifurcation locations, types, and stability properties, as well as overall response curve shape, as explicit design objectives within continuation-based optimization. The second extends sensitivity analysis to solution families defined implicitly as curves and surfaces in parameter space, enabling efficient gradient-based tailoring of dynamic response to engineering specifications. The third develops shape-aware metrics based on differentiable time-series alignment and graph neural networks for quantifying response similarity when exact point-by-point matching is neither achievable nor physically meaningful. Contributions will be validated through numerical implementation and experimental demonstration of optimization and system identification tasks on microelectromechanical resonator systems and aeroelastic structures. The resulting open-source tools and design principles apply broadly to energy harvesting, neuromorphic computing, and any engineered system whose performance depends on nonlinear dynamic behavior. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.